Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations

José Daniel López-Barrientos, Ekaterina Viktorovna Gromova and Ekaterina Sergeevna Miroshnichenko
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José Daniel López-Barrientos: Facultad de Ciencias Actuariales, Universidad Anáhuac México, Huixquilucan, Edo. de México 52786, Mexico
Ekaterina Viktorovna Gromova: Department of Applied Mathematics, St. Petersburg State University, Saint Petersburg 198504, Russia
Ekaterina Sergeevna Miroshnichenko: Bwin Interactive Entertainment AG, 1030 Vienna, Austria

Mathematics, 2020, vol. 8, issue 7, 1-29

Abstract: This work presents a two-player extraction game where the random terminal times follow (different) heavy-tailed distributions which are not necessarily compactly supported. Besides, we delve into the implications of working with logarithmic utility/terminal payoff functions. To this end, we use standard actuarial results and notation, and state a connection between the so-called actuarial equivalence principle , and the feedback controllers found by means of the Dynamic Programming technique. Our conclusions include a conjecture on the form of the optimal premia for insuring the extraction tasks; and a comparison for the intensities of the extraction for each player under different phases of the lifetimes of their respective machineries.

Keywords: differential games; random time horizon; time until failure; discounted equilibrium; weibull distribution; chen distribution; equivalence principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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